Source-observer Distance Research Articles

How Do Schumann Resonance Frequency Changes in the Vertical Electric Field Component Reflect Global Lightning Dynamics at Different Time Scales?

AbstractThe electromagnetic waves in the Schumann resonance (SR) frequency range (<100 Hz) radiated by natural “lightning antennas” excite the Earth‐ionosphere cavity confined between the Earth's surface and the lower ionosphere. The peak frequencies of SR are known to vary with source‐observer distance (SOD), while the daily frequency range (DFR: fmax − fmin) is also indicative of the average size of thunderstorm regions. This paper provides observational evidence for these relationships based on SR frequency observations of the vertical electric (EZ) field component at Nagycenk (NCK), Hungary in Central Europe from the period 1994–2015. Variations of the peak frequencies are considered on the annual, seasonal and diurnal time scales as well as during a specific event when squall‐line formation of lightning activity in South America moves toward NCK. DFR is studied in relation to the El Niño Southern Oscillation (ENSO). Increasing area of lightning activity in mid‐high Northern hemisphere latitudes has been identified by DFR variations during the transition from warm to cold episodes of the ENSO in 1998 and 2010. The extension of the lightning area is considered as a consequence of energy released in the tropics and exported to higher latitudes with some months of delay from the end of the El Niño episodes. The frequency variations are interpreted via model calculations and supported with satellite‐based optical lightning observations (Optical Transient Detector, Geostationary Lightning Mapper). The described variations of SR peak frequencies and DFR yield information on the global/regional lightning dynamics and on this basis they have important application to climate issues as well.

Long-Term Observations of Schumann Resonances at Portishead (UK)

Constructive interference of lightning-generated signals in the extremely low frequency (ELF) below 100 Hz is the source of a global electromagnetic phenomenon in the Earth’s atmosphere known as Schumann Resonances (SR). SR are excited at frequencies of 7.8, 14, 20, 26, … Hz, and their diurnal and seasonal intensity variations are largely dependent on changes in the location and magnitude of the major lightning centres in Southeast Asia, Africa, and South America. In the last five decades, extensive research has focused on reconstructing the spatial and temporal evolution in global lighting activity using SR measurements, and more recently on analysing the links to climate change, transient luminous events (TLE), and biological systems. In this study, a quasi-electrostatic antenna, primarily designed as a thunderstorm warning system, is for the first time applied to measure background variability in the SR band at an urban site in Southwest England. Data collected continuously from June 2015 for a 5-year period are suitably filtered and analysed showing that SR is the dominant contribution to the fair-weather displacement current measured by the sensor in the band 10–45 Hz. Diurnal and seasonal signal amplitude variations have been found to be consistent with previous studies and show the African-European lightning centre to prevail due to the shorter source-observer distance. Also, it is shown that long-term global changes in the ocean and land temperature, and the subsequent effect on the major lightning hotspots, may be responsible for the inter-annual variability of SR intensity, indicating that the largest increase occurred during the 2015–2016 super El-Niño episode.

Model sub-ionospheric ELF – VLF pulses

The propagation of natural wide-band pulsed radio signals in the spherical Earth – ionosphere cavity is numerically simulated. The frequency band considered is 1–10,000 Hz. We address the TM waves originated from a vertical lightning stroke of the Bruce and Golde, Williams, or Jones model. Major data are based on the Williams’ lightning model. The upper boundary of the cavity is horizontally stratified and the conductivity of each stratum depends on its altitude. We apply several models of vertical conductivity profile, and all of them adequately describe the global electromagnetic (Schumann) resonance. The electromagnetic fields are expanded into a series of normal waves (modes). The frequency dependence of the complex propagation constant of each mode is found by using the full wave solution in the form of Riccati equation. The roots of this equation are found by iterations. Various source–observer distances are used in the waveguides with different height conductivity profiles. The Fourier transform of complex spectra provides the time domain realizations of the wide-band pulsed signals. The results of different model profiles are compared and their correspondence to the known observational data is demonstrated. Computations show that the model pulses similar to either tweek or to slow tail atmospherics. They acquire the form of slow tail atmospherics when the conventional night or day conductivity profiles are used. In this case, a train of VLF oscillations precedes a typical Q-burst. The delay of Q-burst from the VLF precursor grows in proportion to the source – observer distance. The tweek atmospheric emerges combined with the Q-burst when the mesosphere conductivity profile has a section of rapid conductivity increase by 4–5 orders of magnitude in the altitude interval of a few kilometers around 90 km.

Studies on Schumann Resonance Phenomena and Some Recent Advancements

Discrete spectra of frequencies at 8, 14, 20, 26, … Hz are generated by electromagnetic emission from lightning sources and can be regarded as excitation of AC global circuit. These electromagnetic emissions originating within the Earth-ionosphere waveguide occur in the ULF, ELF and VLF frequency ranges. These include Schuman Resonances (SR), ELF-VLF sferics, sprites etc. During 1990s and later, the scenario with these sub-ionospheric ELF SR waves changed and several new aspects emerged. The SR power varies with respect to the receiver position and the lightning centers, commonly referred as source-observer distance. Both electric and magnetic components of SR intensity vary with the spatial shifts of the thunderstorm regions under El-Nino and La-Nina conditions. The magnitude of the lightning in the lower atmospheric region varies with time of the day. The electromagnetic waves thus generated at SR frequencies resonate due to multiple reflections in the Earth-ionosphere cavity. The total signal may be dependent on the waves from the different lightning sources. In this context, different groups of researchers throughout the globe are working and published few interesting results. In this work, few results of different observatories are discussed. Also, an attempt was made to detect experimentally the discrete signals at Kolkata (Lat. 22.56° N, Long. 88.5° E) from the year 1999. Some frequency changes in the peak values are observed in the recorded data which may be attributed to uncertainty arising from spatial distribution of lightning sources exciting the Schuman Resonance modes. Some of those results are also presented in this paper.

Efficient Evaluation of the Finite Part of Pole-Free Sommerfeld Integrals in Half-Space Problems with Predefined Accuracy

This communication presents a novel, simple, and robust approach for the computation of the finite part of pole-free Sommerfeld integrals (SIs) in half-space problems with high and controllable accuracy over a large range of source-observer distances. The approach includes the following techniques: 1) cancellation of the branch-point singularities based on the square root change of variables for numerical integration; 2) approximation of real-axis integration path in order to enhance the singularity cancellation for arbitrary low-loss dielectrics; 3) thresholds for truncation of the interval of integration for given accuracy, which improve the efficiency of computation; and 4) prediction formulas that estimate the required number of integration points for a given accuracy up to 1000 wavelengths of source-observer distance. The proposed approach is verified through numerical examples and comparison to reference methods.

Analytical Expressions for Spatial-Domain Green’s Functions in Layered Media

Accurate and efficient formulas for computing spatial-domain Green’s functions are presented in this paper. To apply the formulas, we only require a set of sample points of the spectral-domain Green’s function (SDGF) on an integration path avoiding its singularities and an infinite domain tail path. Since the sampling is carried out for the integrand excluding the Bessel function, the number of sample points required is much smaller than the numerical integration method. This aspect of the proposed method proves to be very advantageous for evaluating closed-form Green’s functions at large source observer distances. It is shown that the proposed formulas provide accurate results for both the near- and far-field regions as well as a wide range of material parameters such as lossless, lossy, left-handed materials as well as multilayered substrates.

Variability of Schumann resonance parameters observed at low latitude stations in China

This paper presents a comprehensive analysis of the Schumann resonance (SR) parameters observed at low latitude stations in China for the first time. Variations of SR peak frequency and intensity on different timescales (from minutes to years) are analyzed in detail. Diurnal and seasonal variations are shown and the source-observer distance is calculated to confirm the contributions of lightning activity. Differences in the profiles of SR intensity between the NS and EW components are due to the effects of the source-observer distance and the relative position of the observer to the sources. Diurnal frequency variations are more complicated and cannot be directly linked with the three thunderstorm centers. Seasonal variations are clear for intensity but not for frequency. The differences in the diurnal and seasonal variations between the SR intensity and frequency show that the greatest contributor to SR intensity is global lightning activity, while the SR frequency is not affected solely by lightning, as certain other factors involving ionosphere properties may play non-negligible roles. We also emphasize that our observations do not show a distinct day–night change in the SR parameters, and that the SR intensity does not show abrupt changes across terminators. This observation is consistent with previous simulations. Finally, the response of the SR to a solar flare is discussed. The flare leads to a sudden increase of about 0.2Hz relative to the 2σ level of the SR frequencies in the first three modes, which is in agreement with other works in the literature. This frequency enhancement is explained using theoretical calculations.

116 THE EFFECT OF LENALIDOMIDE ON HEALTH-RELATED QUALITY OF LIFE (HRQOL) IN PATIENTS WITH MDS: RESULTS FROM THE MDS-005 TRIAL

This paper presents a comprehensive analysis of the Schumann resonance (SR) parameters observed at low latitude stations in China for the first time. Variations of SR peak frequency and intensity on different timescales (from minutes to years) are analyzed in detail. Diurnal and seasonal variations are shown and the source-observer distance is calculated to confirm the contributions of lightning activity. Differences in the profiles of SR intensity between the NS and EW components are due to the effects of the source-observer distance and the relative position of the observer to the sources. Diurnal frequency variations are more complicated and cannot be directly linked with the three thunderstorm centers. Seasonal variations are clear for intensity but not for frequency. The differences in the diurnal and seasonal variations between the SR intensity and frequency show that the greatest contributor to SR intensity is global lightning activity, while the SR frequency is not affected solely by lightning, as certain other factors involving ionosphere properties may play non-negligible roles. We also emphasize that our observations do not show a distinct day–night change in the SR parameters, and that the SR intensity does not show abrupt changes across terminators. This observation is consistent with previous simulations. Finally, the response of the SR to a solar flare is discussed. The flare leads to a sudden increase of about 0.2 Hz relative to the 2σ level of the SR frequencies in the first three modes, which is in agreement with other works in the literature. This frequency enhancement is explained using theoretical calculations.

Comment on “Worldwide extremely low frequency magnetic field sensor network for sprite studies” by Toby Whitley et al.

Comment on “Worldwide extremely low frequency magnetic field sensor network for sprite studies” by Toby Whitley et al.

Numerical study of time domain analogy applied to noise prediction from rotating blades

Aeroacoustic formulations in time domain are frequently used to model the aerodynamic sound of airfoils, the time data being more accessible. The formulation 1A developed by Farassat, an integral solution of the Ffowcs Williams and Hawkings equation, holds great interest because of its ability to handle surfaces in arbitrary motion. The aim of this work is to study the numerical sensitivity of this model to specified parameters used in the calculation. The numerical algorithms, spatial and time discretizations, and approximations used for far-field acoustic simulation are presented. An approach of quantifying of the numerical errors resulting from implementation of formulation 1A is carried out based on Isom's and Tam's test cases. A helicopter blade airfoil, as defined by Farassat to investigate Isom's case, is used in this work. According to Isom, the acoustic response of a dipole source with a constant aerodynamic load, ρ 0 c 0 2, is equal to the thickness noise contribution. Discrepancies are observed when the two contributions are computed numerically. In this work, variations of these errors, which depend on the temporal resolution, Mach number, source–observer distance, and interpolation algorithm type, are investigated. The results show that the spline interpolating algorithm gives the minimum error. The analysis is then extended to Tam's test case. Tam's test case has the advantage of providing an analytical solution for the first harmonic of the noise produced by a specific force distribution.

Reply to comment by A. P. Nickolaenko and M. Hayakawa on “Sprite lightning heard round the world by Schumann resonance methods”

Reply to comment by A. P. Nickolaenko and M. Hayakawa on “Sprite lightning heard round the world by Schumann resonance methods”

A global lightning location algorithm based on the electromagnetic signature in the Schumann resonance band

A new improved algorithm has been developed to geolocate intense lightning flashes around the globe. The method uses ELF (extremely low frequency) radiation propagated in the Earth‐ionosphere cavity to locate unusually intense lightning strokes. Two parameters are needed to locate the lightning discharge from a single station: bearing and source‐observer distance (SOD). The bearing was obtained using the Poynting vector (E × H), while the SOD was obtained on the basis of the modeling of the electric and magnetic ELF spectra and the comparison with experimental data. To check the accuracy of our algorithm, we used primarily infrared cloud top temperature images of deep convective storms from geostationary satellites (METEOSAT, GOES, and GMS). Analysis of ELF data from our field station of 147 events gave an average source‐observer distance error of 660 km (7.05%) and azimuth error of 1.9°. Of the 147 events, 72% had positive polarity, while the majority (59%) occurred over the oceans.

Natural ELF Pulses in the Time Domain: Series with Accelerated Convergence

We present an algorithm for accelerating the convergence of the time domain formal solution constructed for the natural electromagnetic pulses propagating in the Earth-ionosphere cavity. Such pulses originate from vertical lightning discharges and travel around the globe at extremely low frequencies (ELF). A compact formula is found for horizontal magnetic field component. Results of computations are demonstrated for a set of the source-observer distances and properties of time domain solution are discussed.

Green's functions in lossy layered media: integration along the imaginary axis and asymptotic behavior

This paper presents an efficient technique for evaluating Green's functions associated to layered media, when formulated as Sommerfeld integrals in the space domain. The key step in the formulation is that Sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane. It is shown that with this original choice of the integration contour, the numerical effort usually involved in the evaluation of Sommerfeld integrals can be greatly reduced, specially when large source-observer distances are involved. One asset of this technique is that it can be easily incorporated into integral equation based CAD packages for the efficient analysis of complex printed microwave circuit and antennas. In addition, the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media Green's functions for large source-observer distances.

Natural electromagnetic pulses in the ELF range

We analyze the propagation of electromagnetic waves in the ELF. We apply the modal solution for the spherical Earth‐ionosphere cavity and obtain the time domain fields using the FFT algorithm. The Schumann resonance amplitude over the frequency‐distance plane consists of summits and depressions exhibiting separate extended zones. When the source‐observer distance is small, the field maximum is found at some hundred hertz. This component rapidly decays with the distance. The time domain ELF pulse travels with a constant velocity and “bounces” from the source antipode. Its width increases along the path due to absorption of the high frequency component. The distance dependence of the pulse amplitude depends on both the geometrical focusing and the high frequency absorption.

Parameters of global thunderstorm activity deduced from the long-term Schumann resonance records

Abstract Parameters of global thunderstorm activity are deduced from long-term frequency and amplitude records of the first three Schumann resonance (SR) modes performed at the Nagycennk Observatory (47.6°N, 16.7°E), Hungary, from May 1993 to May 1996. The variations of the daily frequency range of each mode, which are characteristic of the changes of the effective source width, exhibit annual and semiannual variations. Annual and semiannual variations are present in both the recorded data and the parameters of global thunderstorm activity. The effective source width varies over 3–4 h at solstices to 5–6 h during the equinox conditions. A period of about four months also appeared in the spectra of the recorded data. A similarity was found between the patterns of the annual and semiannual variations of the daily frequency range, and the changes in median solar time, apart from a three-month phase lead of the astronomical data. The similarity might be due to an unknown solar-terrestrial link. Two approaches were used for the parameterisation of the global thunderstorm activity. One of these employs the preliminary evaluation of the source-observer distance (SOD) using the ratio of individual mode amplitudes. Variations of the source intensity are obtained after dividing the amplitude recorded by that calculated for the established SOD. The second approach applies a direct summation of the individual mode intensities. Numerical simulations showed that such cumulative intensity depends on the level of the global thunderstorms rather than on the SOD. The two estimates were compared and the conclusion was made that these coincide to within ±30%. The maximum of the global thunderstorm activity occurs in summer, in the Northern hemisphere, and the minimum is observed in winter with a two-fold characteristic variance.

Evaluation of microstrip Green function

A new technique for the evaluation of the microstrip Green function, which is generally represented by time-consuming Sommerfeld integrals, (SIs) is introduced. The Bessel function argument-multiplication theorem is used to expand the integrals into a power series. This representation can drastically improve the convergence of SIs. Numerical examples studied indicate that this series-form of Green function gives extremely accurate results, < 0.1% error for all substrates and source-observer distances, using a few terms in the summation series.

Seismic source functions for explosions in a non-spherical cavity embedded in a scattering environment: application to the regional discrimination of nuclear explosions and earthquakes

A quantitative theory is advanced to account for the non-isotropic linear source effects of underground nuclear explosions. Both the cavity's non-sphericity and the scattering caused by source-induced inhomogeneities are considered. Starting with the vector elastodynamic equation for inhomogencous media, the Born-Rayleigh approximation is used for a regime in which the radiation's wavelength is large compared with both the cavity's size and the dimensions of the scatterers but small relative to the source observer distance. Applying the general vector Huygens representation theorem, the total field is expanded in a triple-infinite multipole sum of vector spherical harmonics with summations representing the source, medium and field. When the dust settles over this intricate and complex analysis, there emerges an equivalent localized force system consisting of a singlet force plus a symmetric moment tensor, the elements of which depend on the scattering matrix of the source as well as on its non-sphericity. The moment tensor, in turn, is reducible to an arbitrarily oriented compensated linear vector dipole and a double-couple. Once the equivalent force system is obtained in closed form, the separate contributions of body waves and surface waves are routinely derived and expressed in terms of the source elements. The solution shows that, in addition to the standard explosion-generated P waves and Rayicigh waves, shear displacements, in the form of SH, Lg and Love waves, are exhibited, the amplitudes of which strongly depend on the scattering coefficients and the source's non-sphericity. The theory is applied to explain the observed Lg/Pn spectral ratios and it is suggested that these ratios be employed as a diagnostic tool in the discrimination of explosions from natural seismic events. Provided that an adequate inversion procedure is formulated, the spectral ratios can be used to obtain the explosion source parameters. Beyond the applicability of our analysis to the discrimination problem, the theory developed enables a formulation of a new class of problems in which complexities in source geometry and media physics can be treated simultaneously under a uniform mathematical formalism for a variety of boundary, source, and near-source conditions.

Temporal variations of the global lightning activity deduced from the Schumann resonance data

Temporal variations of the global lightning activity were deduced from long-term Schumann resonance (SR) continuous records. The intensities of the horizontal magnetic field component in the vicinity of the first, second, and third SR modes were monitored at Tottori observatory (35.5°N, 134.33°E) from 1968. Variations of the effective source-observer distance were estimated using the ratios of the intensities of individual modes. This allowed us to obtain average diurnal variations of the global lightning activity for each month over a one-year period. The results show that the distances estimated between the field-site and the effective source are very stable, while the temporal changes of the fields and the global lightning intensity derived demonstrate substantial variability.

The generation of quasi-dynamical accelerograms from large and complex seismic fractures

Abstract The role of the complexity of the seismic source in the generation of near-field high-frequency ground motion is explored. To this end, large (20 km with a resolution of 100 m) and complex seismic fractures are generated with a stochastic growth model depending on two parameters. Synthetic accelerograms are then generated in a high-frequency approximation in which only abrupt changes in the speed of the rupture front are considered. Slip is uniform except for a ramp at the rupture front, and the Green function for a homogeneous, infinite medium is considered. The approximate records are first compared with exact ones and shown to be in excellent agreement for source-observer distances larger than one or two wave-lengths. Examples for different geometries are given that exhibit the dependence of parameters such as peak acceleration, strong-motion duration, and polarization on the observer9s azimuth for a given event. Average records are computed for 1000 events on a 100 by 100 grid; average accelerations do not show a strong azimuth dependence, but peak accelerations vary up to a factor of 5 due to distance and directivity effects. Fourier amplitude spectra for acceleration are computed at a distance from the source half the size of the rupture zone fully taking into account its finiteness. Spectra rise linearly with frequency for a step-like rupture and, for a rupture front lasting about 10% of the total rupture time, they first rise linearly and, at frequencies higher than the risetime, flatten out in agreement with the partial stress drop model of Brune (1970) and consistent with an ω −2 fall-off for displacement.